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⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⣾⠧⠤⠀⠸⣿⡗⢀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢼⠃⠀⠬⠏⠰⠂⠀⠀⠤⠄⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⢧⡀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢓⡆⠀⠀⠀⠀⠀⠱⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠱⣄⠀⠀⠀⢸⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠹⡀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠳⢤⡀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢃ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢄⣠⠏⠻⡆⠀⡀⠈⢢⡞⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠜⠁⠀⠀⠹⣄⠑⣤⠞⠲⡀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠿⠷⠤⣄⡗⠀⠀⠀⠀⠀⢀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠑⠒⠒⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⣴⠤⠒⠀⠀⠀⠀⠀⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⣤⠊⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⣀⠤⠤⠐⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠉⠏⠉⠒⡖⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⠁⠀⠀⣊⠀⢡⠀⠈⢦⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠂⠀⠀⠀⠣⠤⠊⠀⠀⢠⣵⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠰⢄⢂⣠⢦⠐⠂⠙⢭⠦⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡠⠁⠩⢓⡦⠤⠭⠞⠉⠑⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢁⠀⠐⢫⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠂⠀⠀⠀⠀⠈⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀ ⠀⣠⡞⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠀⡈⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀ ⡰⠹⠀⠀⢀⣸⡤⢀⣀⣀⣀⠤⠚⠁⠀⠀⣰⠠⠊⢀⣠⣊⣀⣉⡷⠀⠀⠀⠀⠀ ⠳⢂⣀⠔⠉⠀⠈⠑⠲⣉⣀⣀⣀⡤⠴⠾⠗⠒⠊⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣾⠗⠀⠀⠀⠀⠀⡆⡀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⣤⠇⠀⠀⠀⢠⣾⠿⣿⠛⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣥⣴⣦⣤⣀⠘⣿⣷⠏⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠿⠿⢿⣿⣷⣄⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⣾⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠈⢻⣿⣇⢸⣿⣿⠀⠀⠀⠀⣀⠀⠈⠙⣷⣶⡄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣠⣤⣄⣀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⣿⣿⠀⠀⠀⠀⡿⠿⠶⣶⣿⣟⢷⣄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⡿⠿⠿⠿⣿⣷⣦⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⡄⠀⠀⠀⣿⣷⣶⣼⣿⣝⣿⡃⠀⠀⠀⠉⠙⣿⣿⠟⡛⣡⣤⣀⠀⣀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⠏⠀⠀⠀⠀⠈⠹⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠈⠿⣿⣍⡁⠀⠀⠀⠀⢀⣿⡇⢰⣾⢷⣯⠻⣷⣿⠇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣶⣾⠿⢿⣷⣄⣹⣧⣹⣿⣿⠿⣧⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⢻⣿⢿⡟⠙⠇⠀⠉⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⢠⣿⡟⠈⠁⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡁⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⣶⣶⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠿⢿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠙⢿⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠈⢿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠸⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⢀⣴⣿⣿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢰⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣿⠿⢿⣿⣶⣤⣀⡀⠀⠀⣀⣰⣾⡿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣉⣠⣤⣤⣤⣶⣶⣶⣾⣿⣿⠿⠟⠉⠁⠀⠀⠉⠻⠿⢿⣿⣿⣿⣿⠿⠏⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣤⣶⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢀⣠⠤⠒⣚⣿⠟⠹⣯⣝⢓⣒⣤⣀⣀⠔⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣨⠗⢯⡤⠐⠚⠛⢥⡀⠀⢠⡟⠉⠀⠈⠙⢿⢶⡊⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡜⠉⠒⡾⢤⡀⠀⠀⠀⠹⡀⣿⠉⢣⡀⠀⠀⠘⡖⠻⡍⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠉⠙⣧⡀⣷⡀⠀⠀⢀⣗⣸⣶⣾⣧⠀⠀⣰⠃⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⠿⣿⣇⢀⣠⠾⡿⣿⢏⡙⢷⣶⠾⣁⡀⠀⢸⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠼⠄⠀⡤⠄⠒⣺⢿⡝⠀⠁⠉⠛⠋⠁⠈⠳⡑⠢⠬⠉⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠰⠒⢉⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠜⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⢲⠚⡏⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣎⠉⠒⠤⣀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢀⠇⠀⠀⠀⠀⢸⠀⠘⢄⡀⠀⠀⠀⠀⠀ ⠀⢀⡴⠥⠤⠉⠑⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⡼⠤⠤⠴⠬⠽⠶⢤⠄⠀ ⠠⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠤⢖⡶⠖⠊⢁⠄⣰⠀⠀⢸⠒⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⡢⢔⠠⠠⢟⠈⢻⠖⠚⢴⣥⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⡞⠂⠀⠀⢣⢍⣀⠀⠀⡃⠩⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢾⡀⣠⢷⡾⠻⠤⣔⠁⠀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⠃⠀⠀⠉⠀⠈⠡⠂⠕⠀ ⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠠⠐⠁⠀⠀ ⠀⢠⠒⠤⡀⠠⠁⠀⠀⠀⠀⠀⢀⠌⠀⡠⠀⠀⠀⠊⢄⠀⠀⠀⠀ ⠔⠃⠀⠁⠀⠁⠀⠀⠀⢀⢀⠀⠁⡀⠠⠁⢀⣀⠐⠁⠐⠈⠑⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⠉⠉⠉⠉⠉⠉⠑⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣞⣉⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⠙⠂⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⡴⠛⠉⠙⢻⣦⡀⠀⣠⠞⠉⠀⠉⠻⣶⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⢸⡇⠀⠀⠀⠀⣿⣷⠀⣿⡀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠘⣷⣤⣀⣠⣞⣹⠇⠀⢿⣷⡦⠤⠴⣇⣨⡏⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠟⠀⠈⠛⠲⣶⣿⣁⣀⡀⠀⠙⠣⠀⠤⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⢀⠤⠿⠟⠻⣿⣷⣷⣶⣃⣴⣷⣶⣶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣹⠉⠉⠙⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⡀⠀⣠⠔⣻⠛⠉⠧⢬⠟⠙⢯⠙⠻⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠾⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠑⠒⠒⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⡗⠢⢄⣀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⡇⠀⠀⠈⠉⠓⠲⠼⢦⡀⠀⠀⠀⠀⣧⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣀⡼⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⣀⡤⣾⠋⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠤⠔⠒⠊⠁⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠛⠒⠒⡲⢺⠗⠒⢒⠒⢒⣀⣠⠀⢤⢿⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠰⠖⠶⠶⠶⠶⢶⡶⠀⠈⠉⠉⠁⠀⠘⣆⠀⠀⣀⠔⠁

⠀⠀⠀⡠⠐⠂⠉⠉⠉⠉⠁⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⢊⣉⣉⠀⠀⢀⡠⣁⡂⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢱⠁⠀⢸⣧⢰⡃⠀⠀⣿⡄⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠘⠷⣀⡪⠏⠘⢷⡒⣺⠼⠁⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠤⠖⣺⣿⢯⣣⡶⣆⣄⠀⠀⠀⠀⠀⠰⢩⠀⠒⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⢔⡨⠋⠀⠁⠀⠑⠈⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀⠈⢼⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⠰⠐⢄⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠠⣀⠀⠀⠰⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢠⠉⠒⠠⠜⣄⠀⠀⠸⣀⣀⣀⠀⠀⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠊⠀⠀⠀⠀⠀⠑⠂⠀⠃⠀⠀⠈⡆⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠀⠀⠀⢠⡆⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⠠⠔⡚⠁⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠄⡀⠂⠁⠀⠀⠐⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠥⠮⠥⢤⠎⠒⠒⠘⢇⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠁⠙⡌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⡄⠀⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⡦⢿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠃⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠀⢸⣀⣠⣤⣀⡇⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⡼⠀⠳⣍⡲⣌⢙⣆⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⡤⠾⣄⣀⣀⣈⣉⡽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⣀⡤⠴⠒⣛⣯⡟⠙⣿⣍⡙⠓⠲⠤⣄⡀⠀⢠⡤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⠲⣤⡔⠋⢁⣀⡤⣾⣛⠋⠁⠀⠈⠙⣿⠗⠛⠙⠒⢯⡷⣏⣀⡴⠞⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣞⠉⢙⡶⠋⠁⠀⠀⠉⠳⣄⠀⠀⣾⣅⡀⠀⠀⠀⠀⠙⣏⠻⣄⣀⣠⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣼⡁⠈⠙⡾⠓⢦⠀⠀⠀⠀⠀⠘⣆⠀⣇⠀⠹⡄⠀⠀⠀⠀⢹⠋⠙⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠉⠉⠛⣧⠀⠈⣧⠀⠀⠀⠀⠀⣽⠄⢻⣦⣴⣿⡄⠀⠀⠀⣼⠀⠀⠸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⣾⣿⡇⠀⠀⠀⣴⣷⣷⣾⣿⢿⣿⣃⣀⣠⠞⠁⠀⠀⠀⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⠛⢿⣥⠤⡴⠛⡍⢯⣙⣏⣫⡆⠘⣬⡏⣝⠒⠦⢤⣀⡀⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠼⠇⠀⠠⠴⠒⠚⢉⡥⢞⣧⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠻⣌⠙⠒⢤⡄⣸⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢰⠔⠚⢉⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣠⠤⠞⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠙⠲⢤⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠘⡆⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠉⠑⠒⠤⡀⠈⠓⢦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣉⠓⠲⢤⣀⡀⠀⠀⠀ ⢀⡴⠋⠉⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⣴⠟⠒⠒⠒⠛⠓⠒⠒⠚⠛⠛⠀⠀ ⠞⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⣲⠶⠚⠉⢀⡴⠀⣸⠀⠀⠀⣸⠓⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡋⠉⣽⠲⠤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⠓⠃⠀⠀⣰⡴⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢠⠎⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⡇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⢠⠃⠀⠀⢸⠀⠀⢠⢯⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⡠⠋⠀⠀⠀⡸⢀⡴⠋⢸⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⢀⡾⢔⡋⠀⢀⡴⠛⠁⢧⡀⠈⠓⢤⡀⠀⠀ ⣴⣋⠀⠀⢠⣆⣀⡠⠤⠤⠔⠻⠯⠭⠴⠒⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀ ⠉⢹⡀⠀⠀⡩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠳⢤⣙⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠋⣩⡛⠉⠙⠻⠿⣿⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠀⠀⠀⠉⠁⢀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠄⠀⠀⣾⣟⣿⣦⠀⠀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⠛⠛⠛⠒⠀⠀⢿⡟⢻⣿⡇⠀⠭⠃⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⢰⣶⣦⡄⠀⠀⣀⡀⠙⠛⠋⠀⠀⢀⣴⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⣀⣿⠉⠁⠀⢀⡌⠂⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⣄⠀⠑⠒⣺⠍⠀⠀⠀⠀⠀⢀⡄⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⣇⢿⣶⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠼⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡏⣀⢻⡧⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡵⣫⣽⠤⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠀⠀⢡⣬⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡞⠛⢁⡠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡈⠻⣿⣷⠈⣓⠲⢤⡤⢄⣀⣀⣀⣀⠤⠤⠔⠛⠋⣶⣉⣉⣉⡱⠤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠈⣁⠀⠈⠱⠄⠁⠙⠃⠀⠀⠀⠀⠀⠀⢀⡼⢷⣤⣄⣠⣤⣖⣛⣢⣄ ⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠢⠭⠏⠁⠉⠙⠿⠺ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣴⡶⠒⠒⠒⠊⠀⠈⠙⠒⢤⣤⣴⠁⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⣀⡠⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠿⠿⠶⠆⠀⠀⠀⠀⠄⠒⠁⠀⠈⠢⡀⠀⠀⠀⠀⠉⠉⠉⢉⣻⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠐⠒⠚⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠟⠛⠛⠛⠉⠉⠉⠛⠛⠛⠻⠿⠶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⣤⣶⡿⠟⠻⠿⣶⡄ ⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⣼⡇ ⠀⢠⣾⠟⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀ ⢠⣿⠃⢸⣿⣿⣿⡷⢀⡠⠀⠀⠀⠐⠤⡀⠀⠀⢀⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀ ⣾⡇⡴⠒⠙⢟⠛⢱⠋⠀⢀⣀⠀⠀⠀⠈⢆⠀⠘⣿⣿⣿⡿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀ ⢿⣇⣆⠀⠀⡜⠹⣅⣀⣀⣸⢿⡁⠀⠀⠀⠘⣤⠀⠈⢩⠉⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄ ⠈⢻⣮⡉⠉⠀⠀⠘⢍⣉⠓⠖⠛⠒⠲⠖⡞⠁⠀⠀⠈⢆⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿ ⠀⠀⠙⠻⣶⣦⣤⣤⣤⣄⣉⣉⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣤⣤⣤⣶⡶⠶⠶⠶⠶⣶⣶⣶⣶⠾⠟⠁ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣷⣤⣀⠀⠀⠀⠀⣀⣼⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠏⠻⣯⡙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡏⠀⠀⠈⢷⡀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⠀⠀⠀⢸⡇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡘⣦⠀⠀⣸⣧⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⡶⢿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠰⠷⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣏⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⠄⢀⠀⢻⣇⢤⣶⠶⠶⢦⣤⣿⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⢀⣾⠀⠈⢻⣦⡙⠻⣦⣀⠈⠻⣦⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⡾⠃⠀⠀⠀⠉⠻⠷⣶⣽⣷⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣤⣤⠾⠻⢦⣤⣀⣀⣀⣀⣀⣠⣤⡤⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠄⠂⡝⠉⠛⠳⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣶⣆⠀⢠⣶⣄⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢟⡉⠁⠂⠘⣉⡿⠀⠛⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⣘⡟⠁⢀⠂⠀⠀⠀⠈⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡦⠬⠍⠃⠀⠀⢀⢠⡐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡆⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢼⢉⠿⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣐⢝⡽⠌⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠠⠸⣾⡖⠤⢀⣀⠀⠀⢀⣀⠼⢯⠔⠁⣄⡀⠀ ⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠳⠌⢅⠈⠂⠁⠃⠀⠀⠀⢀⠚⠦⢤⠶⢷⣦ ⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠁⠀⠀⠁ ⠀⠀⣀⡀⣀⠙⠦⣀⠀⠠⠊⠀⢀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠷⠦⠀⠀⠠⠐⠉⠑⢀⠀⠈⠀⠐⣒⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠛⠉⠉⠙⠻⢶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⣤⡶⠀⢀⣠⡀⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⢸⡏⠀⠀⣀⠀⠀⢀⣹⣵⣤⡸⠞⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠁⠀⠙⣷⣸⡇⠀⢠⣈⣷⡄⠸⣿⣿⣿⣿⠂⠀⢸⡇⠀⠀⠀ ⢠⡾⠛⠛⢷⣾⠁⠀⠀⠀⣿⠹⣧⠀⠘⠒⢿⡏⠀⠈⣿⢻⣵⣄⡄⣾⠁⠀⠀⠀ ⣿⠀⠀⠀⠀⠉⠀⠀⠀⣼⠏⠀⣿⠀⠀⠀⠀⠙⡗⠚⠛⢾⣿⠿⠓⢻⡆⠀⠀⠀ ⢹⣆⠀⠀⠀⠀⠀⢠⣾⠋⠀⢀⡿⠀⠀⠀⠀⠀⢧⣀⣠⡟⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠙⠻⢦⣤⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣦⠀ ⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠹⣧ ⠀⠀⠀⠀⠀⠈⠻⣦⣠⡶⠟⠛⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢀⣤⣾⡃⠀⠀⢀⡿ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠀⠀⢀⣠⣴⣿⣤⣤⡶⠶⠟⠋⠁⠉⠛⠷⠶⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠐⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⣀⣀⡈⠣⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠃⠀⣠⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠛⡻⠃⠀⠀ ⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡲⠞⠋⠙⡄⠀⠀ ⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠉⠉⢸⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢳⠂⠀⢾⠁⠀⠀ ⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⡇⠀⣄⠀⠱⡀⠀ ⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡇⡴⠃⠓⠶⠃⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠚⠉⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⠭⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠷⠒⠋⠉⢀⣠⠴⠃⠀⠉⠑⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢷⣠⠴⠒⠉⠁⢀⣴⣾⡇⠀⠀⠀⣙⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠯⠟⠋⠀⠀⠀⠈⢻⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀

⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠈⠉⡿⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠁⡀⠀⠀⠀⠀⠀⠀ ⠀⠚⠑⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠁⠀⠐⠀⠀⠀⠀⠀ ⣠⢤⣄⢾⣹⠂⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⠓⠛⠛⠛⠒⠶⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⠀⠄⠁⢀⠂⠀⠀⠀⠀⠀⠀ ⠀⣠⠏⠈⡄⠀⠀⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣤⡀⠀⠀⠶⢬⡙⣧⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣁⣀⢰⣲⠄⠀⣠⠞⠁⠀⠀⠀⠀⣴⠚⠲⠟⠁⠩⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣴⡀⠀⠻⠀⠀⠠⠀⠈⠀⠄⠁⠀⠀⠀⠀⠀⠀ ⠈⢉⡝⠀⠉⠐⡼⠃⠀⠀⠀⠀⠀⠀⣇⡄⡶⠛⢲⡌⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠄⣁⡤⢬⣤⣀⣀⢀⣠⣄⡀⠀⠀ ⠀⠊⠀⠀⠠⡾⠁⠀⠀⠀⠀⠀⠀⢰⠋⠀⠳⣤⠼⢓⣀⣵⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣦⠾⠋⢀⡴⠛⢭⣉⣿⢧⣤⣽⣆⡀ ⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⢶⣀⢀⣸⣯⠮⣍⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣄⡴⢛⣭⣭⣤⣦⡾⢿⣤⣎⣧⢰⡦⡿ ⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣋⢿⣀⡿⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⡆⢹⠃⠼⣏⡍⢍⡿⣧⢜⣏⣩⢝⡾⣣⠗ ⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣗⣠⠷⠞⠃⠀⠀⠀⠀⠀⣠⠤⠞⢃⣐⡟⠌⢴⡿⢷⢃⣭⣟⠉⢿⣉⠩⡻⣅⠀ ⠀⣸⠃⣠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣤⢸⠃⠀⡾⠋⣷⢦⣴⢟⣴⡟⠻⢻⠋⠳⣾⢧⡂⣵⠾⠛ ⠀⣿⠄⠀⠩⠋⣡⠀⠀⣴⡄⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⢸⣧⠀⠠⣴⠻⣿⣥⣎⢭⡟⠀⠀⣸⡾⠳⠇⠀⠀ ⠀⠘⢦⡀⠀⠀⠘⠓⣾⠉⣳⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠴⢬⣽⠃⣽⠃⠀⠽⣞⣠⠴⣾⠏⠀⠀⠀⠀⢠ ⡇⠀⠀⠙⠓⠦⣤⣤⣈⣉⣁⣀⢀⡀⡀⣀⢀⣀⣀⣀⣠⣤⠤⠴⠶⠶⢶⠶⢶⣖⠋⠁⠀⣸⢇⣻⠃⠀⠀⠸⡯⣠⠟⠁⠀⠀⠀⠀⣠⠚ ⡇⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠚⠓⠓⠛⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⢸⡆⠸⡏⠰⠦⣴⡟⣊⡟⠀⠀⠀⢀⣷⠟⠀⠀⠀⠀⠀⠀⣯⠀ ⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢀⡇⠄⠀⢼⠗⣸⣧⣀⠀⠀⣸⠃⠀⠀⣀⣀⣀⣠⢼⠋⠀ ⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⣹⠃⠀⠈⢾⣸⣼⣥⡽⠛⠋⠁⠀⢴⠋⠉⠉⠀⠀⢨⠗⠀

⠠⢤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀ ⠒⡇⠛⠀⠀⢀⡤⠔⠚⠉⠉⠉⠉⠉⠙⠒⠤⣄⠀⠀⣔⢤⡀⠂⢀⠀⠁⠀⠀⠀ ⠨⡄⠶⢀⡔⠁⠀⠀⣲⠐⣊⡙⣆⠀⠀⠀⠀⠀⠙⠶⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠁⠀⡌⠀⠀⠀⠀⡜⠘⠤⠇⣠⣇⡀⠀⠀⠀⠀⠀⣈⠧⠜⢉⡽⢻⡻⢭⠷⣄ ⠀⠀⢰⠀⠀⠀⠀⠀⠈⠉⢷⡶⡏⣷⡆⠀⠀⠀⠀⠀⣇⣸⣱⠾⣷⡿⣷⠾⣾⠿ ⠀⡴⠁⡀⠀⠀⠀⠀⠀⠀⠀⠙⠽⠖⠊⢀⡀⠀⡤⢘⣡⠆⣸⢻⣡⣏⡹⡍⠿⣅ ⢰⡀⠙⠛⡀⢠⠀⠀⠀⣶⡦⠀⠀⠀⠀⠀⠈⠺⣀⡇⠉⣽⣽⢇⠶⠃⢹⠷⠏⠁ ⡀⠑⢤⣀⢙⠫⠛⠋⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠼⠘⣞⡵⠁⢸⡵⡺⠋⠀⠀⡰ ⡃⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⡇⢧⠠⢼⣇⠇⠀⢀⡿⠃⠀⠀⢘⡇ ⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡞⠀⢼⣸⣓⠶⠜⢀⡄⠒⠒⢹⠄

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⠶⣶⠸⠷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠄⠀⡈⠀⠐⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠐⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀ ⣠⣤⣤⡄⢾⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠂⠁⠈⠀⡀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠐⡄⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣤⡀⠀⠀⠀⠀⣤⣬⡙⢻⣆⠀⠁⠠⠈⢀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠚⠁⠀⢀⣈⡀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⣀⣤⣀⣰⠾⠛⠷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠈⢻⣦⠛⠀⢀⠐⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡤⢶⣦⠸⠥⠿⡄⢀⣼⠏⠀⠀⠀⠀⠀⠀⠐⣾⠋⠀⠉⣉⣀⠐⢁⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣄⡀⠀⠁⠀⠠⠀⢀⠈⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠇⠀⠀⠀⢈⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣔⢨⡾⠋⠙⢷⡀⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠐⠀⢀⣴⠶⠶⢶⣄⣄⣀⣀⣠⣤⣤⣄⠀⠀⠀ ⠀⠘⠃⠀⠀⠀⢄⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⡟⠁⠘⢷⣄⣠⡿⢀⣁⣰⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣷⣤⣴⠟⠁⠀⣠⡾⠋⣭⠉⣛⣿⣤⣄⣙⣧⣀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣘⣤⡈⠁⠰⢸⡟⣍⣻⠛⢛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⣩⡴⠶⣶⣞⣋⢀⣀⣙⣿⠋⣤⠹⣇⢉⣉⡹⡧ ⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣷⣇⣷⡿⣹⠏⠹⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⣸⡏⡀⣿⠿⠹⠿⢿⣿⡹⠿⣿⠿⢁⢿⣶⣿⢇⡏ ⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡽⠶⢾⠋⠌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡈⢀⣿⢀⡰⢿⣬⡑⡫⢾⡛⣷⣤⣿⣤⣷⣦⣿⣡⡾⠁ ⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣛⡼⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠛⠁⣐⣽⠏⠆⢠⣷⠟⣷⡑⢦⣽⡏⠁⢻⡇⡜⡡⠛⣿⣄⠀ ⠀⢀⡾⠁⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠶⠶⣄⡀⣸⠏⠀⢠⡶⠟⣩⣥⣄⣠⡿⣑⣽⠟⠿⠿⣿⠙⠷⣤⣿⡴⣁⣫⣤⡽⠟ ⠀⢸⡇⠀⠉⠿⠿⠿⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠒⣼⠓⠀⠙⢁⣸⢿⣴⠿⠱⣘⠬⣳⡟⠀⠀⠹⣧⣿⣦⡟⠁⠀⠀ ⠀⢸⣏⠀⠀⠀⠁⠀⢿⣀⣀⣸⣿⣇⠀⠀⠀⣤⠀⠙⠻⠿⠟⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⡿⠒⢀⠐⣽⠟⣪⣿⠛⠛⣷⢶⡟⠀⠀⣀⣴⡿⠁⠈⠁⠀⠀⠀ ⠀⠀⠹⣮⣀⠀⠀⠀⠀⠉⠹⣏⣀⣽⠷⠶⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡇⠻⢶⣾⢯⣘⡾⠁⠀⠀⢙⣏⣤⡶⢞⡿⠋⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠙⠳⠶⣦⣤⣀⣀⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⠶⠶⠶⣶⡶⠴⣶⡶⠛⠉⠀⠀⣸⡏⣎⣼⠃⠀⠀⠀⢸⡟⢡⣼⠟⠁⠀⠀⠀⠀⠀⢀⡴⠞ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠃⠀⠀⠀⠀⠀⠀⢻⡇⠀⣿⡜⢠⣤⣠⣠⣿⢸⣸⡇⠀⠀⠀⠀⠘⣟⣿⠟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠄⠉⠉⣹⡇⢣⣿⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠗⠀ ⠀⠈⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠈⢀⢾⡇⠂⠀⡀⣿⢹⢰⣿⠷⣦⣀⣀⣠⡾⠁⠀⢀⣠⣤⡤⡤⠶⠶⠛⣇⠀⠀ ⠀⠀⠀⠀⠀⠈⡙⠶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⣀⣈⣿⠀⠀⠀⠠⢿⣚⣚⣿⣴⠾⠛⠉⠉⠀⠀⢰⣟⠉⠀⠀⠀⠀⠀⢠⡿⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⢀⡤⠞⠁⠀⠀⠀⠀⢀⣤⣾⠿⠛⠁⠀⠀⠀⠀⠀⣀⡤⠚⠁⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⢘⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁⠀⠀⠀⢀⣴⣶⣶⡴⠚⠁⠀⠀⠀⠀⠀⠀⢀⣴⣾⢵⣾⣿⠟⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠁⢀⣴⣥⡾⠋⠀⠀⣰⣿⡿⠋⠀⣠⣄⠀⠀⠀⠀⢀⣠⠞⢻⣿⣿⠿⠋⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣫⣾⠟⣩⡾⠟⣡⣄⡴⠊⠉⣩⣄⣠⣾⡿⢉⡴⠃⢀⡴⠋⠀⠀⠀⠉⠁⠀⣀⣴⣦⣤⣸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⡶⠞⣩⡾⠛⣱⣿⢏⣴⡿⣻⠟⠀⣠⡾⠉⢈⡿⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⣾⣯⡶⠛⠁⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠒⠁⠀⠀⠀⣀⡤⠚⠁⣠⡾⣿⣴⣿⣿⣷⠟⣫⠞⠁⣠⡴⣋⣠⡶⠋⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣀⡴⠖⠋⠁⠀⠀⠀⣀⣤⡶⣿⣿⠴⠂⣴⢏⡴⠿⠟⠉⠀⠠⠞⠁⢠⠞⣉⣿⠛⢋⣤⣾⢆⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⢀⣠⣶⣿⡿⢋⣽⡿⠃⡀⢘⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢉⡤⠀⠟⠉⣠⢟⣤⣾⣷⣶⣶⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡿⢇⡀⠀⣀⣴⣶⣿⣾⡿⠁⣰⣿⠟⢀⣼⡵⠋⠀⢀⠄⠀⠀⠀⠀⠀⠀⠠⠊⢠⡾⠃⠀⠀⠸⠇⣼⠟⢉⣴⣿⣿⣩⡏⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⢹⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢷⡀⣿⡄⠀⢻⣿⡒⢁⣷⣼⣿⠋⣰⣫⠞⠀⠀⣠⠏⡆⠀⠀⠀⠘⡄⠁⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⡇⢻⣟⣁⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⢧⡹⣿⡦⠈⢻⣷⣼⣿⣿⠃⠀⠋⠁⠀⠀⣰⠃⢸⠀⠀⠀⠀⠀⠇⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠿⢿⣿⠟⣿⣠⣾⠟⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠙⢮⡀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⢀⡇⠁⠀⡇⠀⠀⠀⠀⠸⠀⠀⠸⡄⠀⠀⡀⠀⢀⡴⠋⠀⣰⠃⢠⠿⠃⣠⣿⠏⠁⠀⡇⠀⣀⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⡿⢹⠏⠀⠀⠀⠀⠀⢸⠀⠀⣼⠁⠀⠀⠀⠀⡆⠀⠀⠀⣧⠀⠀⠁⢠⠞⠀⢀⡼⠁⣠⢆⣠⣴⣿⣿⣀⠀⣸⢥⣶⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠃⠸⠄⠀⡄⠀⢠⠀⢸⠀⠀⣇⠀⠀⠀⠀⢰⠃⠀⠀⢰⡟⢀⠀⢀⡏⠀⠀⠘⠀⣰⠃⡼⢹⠃⠀⣾⣿⣾⣿⠘⠛⠙⠙⣳⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⠀⠱⠄⢸⠀⢸⠀⢲⠸⡄⠀⠀⠀⣸⠀⠀⠀⣴⠃⡆⠀⡼⠀⠀⠀⢀⣼⢃⣾⣷⡟⣀⡿⠛⣱⣿⠏⠀⠀⢀⣴⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢰⣿⣷⡀⠀⠀⠸⡄⢸⠀⠈⡆⠇⠀⠀⠀⡋⠀⠀⠀⣿⢰⡷⣶⠃⢀⣠⢶⣞⢀⣾⣿⠏⢠⠟⠀⠀⣿⣿⣶⡇⣠⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⢿⣿⢷⡀⢀⡀⣽⣾⡇⢿⣿⣿⠀⠀⢀⠁⠀⡄⠀⣹⣿⣿⣿⣶⡿⣥⣾⣿⣿⣿⢋⣰⠏⠀⠀⠀⣿⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠈⣷⡜⣆⠹⣄⣿⣿⣿⠿⣟⣿⣿⡀⠀⠈⣆⡼⠀⢀⣿⣿⣿⣿⡷⠬⠙⠻⠇⠛⠛⢻⣷⣶⣶⡆⠀⠙⠟⣿⡟⠁⠀⢀⣠⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣿⡿⣎⠓⠟⢛⣷⣶⣶⣮⡙⢿⣧⠀⢠⡀⡇⠀⢸⣿⢹⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠉⠉⠿⠁⠀⠀⣼⣏⠀⢀⣴⠏⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣆⠘⣧⢠⣾⣿⣿⣿⣿⣇⠘⣿⠀⠀⠙⢷⠀⢸⣧⣼⣿⣿⣿⣿⣿⠃⠀⠀⢀⣶⣿⣿⠀⠀⢀⡞⣽⠋⠓⠻⣅⣀⣀⢀⣠⠾⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣌⣷⢿⣿⣿⣿⣿⣿⡄⣿⠀⢸⢠⡰⠀⢸⣿⠟⠻⣿⣿⣿⡟⠀⠀⠘⠛⠛⠛⠁⢀⣴⣿⠟⠁⠀⢀⢠⣼⣶⣿⡟⠁⠀⣸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣝⣟⣛⣥⠤⢤⣽⡀⠀⠈⢳⡀⢸⣿⣷⣦⣤⣤⣤⣤⣴⠀⠀⣀⣤⣤⣾⣿⠛⣩⣟⣠⠾⠟⠋⠉⢘⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡻⢬⠅⠈⣿⣿⣿⡇⠀⠀⠀⠑⢸⣿⢿⣿⢿⡟⠛⠟⢋⡴⠋⢿⠿⠛⠒⠛⠛⠉⠁⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⢿⠻⢿⠀⠀⠀⠀⣠⠃⠸⣿⡟⠀⢀⣴⠫⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⢹⣿⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⣷⣤⣀⠀⠀⣠⣴⣤⣤⣴⡅⢀⠀⡈⣀⣤⣾⠯⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢊⣡⠴⠚⣉⣉⠭⠽⣿⣿⣿⡄⠙⢿⣿⣿⣿⠁⢈⣿⣿⣿⣟⡛⠒⠦⢤⣉⠑⢦⡀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⣻⣽⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⢀⡴⠊⠁⢀⣠⠤⣘⣿⣧⣾⣆⣀⣙⣿⣁⣀⣨⣿⣿⣾⠋⠉⠙⠲⢤⡈⠙⢦⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⠖⠋⡴⠊⢁⡼⠋⠁⠀⠈⠉⠉⠁⠀⠀⠀⠁⠈⠳⡄⠀⠀⠀⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣴⣯⣤⣾⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⣯⣛⣦⣀⣀⣀⣠⣤⢤⣤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡞⣯⢳⡝⣮⢳⡳⣎⠷⣎⢿⡸⢧⣳⡽⣞⡽⢾⣶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡹⢮⡝⣮⢳⡝⣮⢳⡝⣮⢻⡜⣧⣛⢯⡳⣝⡞⣼⢣⣿⣿⡜⣧⢳⡖⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⢁⣾⡹⢧⡻⣜⢧⡻⣜⢧⡻⣜⢧⣛⢶⡹⣎⢷⣻⣿⡜⣧⣿⣿⡝⣮⢳⡝⣮⡝⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⢶⡲⣞⣻⣿⣿⡟⣧⣛⢧⡻⣜⢧⡻⣜⣧⡿⠚⠳⣽⢎⡷⣹⢎⡷⣹⠾⡿⢿⣫⢞⡵⣫⢞⡵⡻⣜⣏⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡳⣝⢮⡳⣽⡶⣹⢶⡹⢶⡹⣎⢷⡹⣎⠷⣭⣿⣇⣀⣠⣾⡿⣜⢧⡻⣜⢧⡻⣝⢧⣛⢮⡳⣝⢮⡳⣝⠾⣜⡻⣜⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣷⣹⢎⡷⣹⡳⣝⢮⡝⣧⢻⡜⣧⢻⣜⡻⣜⣿⣿⣿⣿⣿⡟⣮⢳⡝⣮⢳⡝⣮⢳⡝⣮⢳⡝⣮⢳⡭⣻⣜⡳⣭⣷⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠻⢿⣾⣵⣫⣷⣹⣎⡷⣹⢎⡷⣹⢮⡝⣧⢻⡝⣿⢻⡟⣯⢳⡝⣮⢳⡝⣮⢳⡝⣮⢳⡝⣮⢳⡽⠊⠁⠉⠙⢧⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⢘⠐⠀⠩⠝⡉⠉⠙⢿⣧⣻⡜⣧⢻⡜⣧⢻⣜⣧⣿⣾⣷⣏⢾⡱⣏⢾⡱⣏⢾⡱⣏⢾⡱⣏⡇⠀⠀⠀⠀⠀⢿⣿⣿⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠌⠀⠈⠄⠄⠀⠀⠀⠈⠀⠄⢙⠻⢿⣷⣿⣾⣷⣿⣿⣿⠟⠏⠁⠉⠚⠵⣫⢞⡵⣫⢞⡵⣫⢞⡵⣫⢞⡄⠀⠀⠀⠘⢸⣿⣿⣿⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠉⠹⡹⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢵⣫⢞⡵⣫⢞⡵⣫⢞⡦⣄⣀⣰⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡳⣝⢮⡳⣝⢮⡳⣝⢮⣿⣿⣿⡿⣿⣿⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢾⣣⢟⡼⣣⢟⡼⣳⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢯⡞⣵⢫⣞⠰⠘⣿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡜⣧⢻⣦⣥⣿⣿⣿⣿⣽⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣿⣿⣿⣿⣿⠎⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣽⣯⠀⠀⠘⣿⣿⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⣿⣿⣷⣿⣿⣿⣆⠀⣠⣿⣷⣯⣾⣝⢯⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢹⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⣿⣹⣲⢤⣄⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣗⣄ ⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣾⣿⣿⣿⣿⣯⣿⣿⣿⣟⣿⣿⣻⣿⣿⢿⣿⣿⣾ ⠀⠀⠀⠐⠎⢢⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠟ ⠀⡀⠀⠀⠈⠂⠑⢄⠀⠁⠀⠂⠤⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⢿⣷⣿⣿⣿⣯⣿⣾⣿⣿⡽⠋⠀ ⢠⠀⠀⠀⠠⠀⠀⡀⠌⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢿⣿⣿⣿⣟⣿⣿⣿⣯⣿⣿⣿⣿⣿⣽⣿⣿⡿⠝⠊⠀⠀⠀ ⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠐⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠙⠛⠛⠛⠿⠿⠾⠿⠿⠿⠽⠞⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⣀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠂⠐⠀⠀⠀⠐⠀⠉⠀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠉⠉⠉⠉⠒⠒⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⣀⡤⠶⠚⠛⠛⠛⠛⠓⠲⢤⣤⣀⠈⠙⠒⠢⠤⠤⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠶⠤⠤⠤⣀⣀⣀⣈⠉⠁⠐⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⡾⠁⠀⠀⢀⡀⠀⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⠦⣄⣀⠉⠐⠦⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠁⢠⠟⠀⠀⠀⠰⠿⠓⣠⣤⡄⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⡀⠙⠢⡀⠀⠀⠀⠀ ⠀⠀⣠⠤⠀⠠⠇⠀⣿⠀⠀⠀⠀⣠⡤⡀⠙⣛⡀⠀⣿⣷⡢⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠈⠢⡀⠀⠀ ⠀⣰⠁⢠⣶⡄⠀⢸⠇⠀⠀⠀⠘⢻⠟⠓⠋⠀⠀⠉⠉⠉⠊⠀⠀⠀⣾⡿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀⠙⡄⠀ ⣰⠁⣠⠿⢏⣛⠟⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢹⠀ ⡷⠀⣿⠀⠀⣿⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⠀⡇ ⢧⠀⠻⢦⣤⣟⣠⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡇ ⠈⠳⢤⣀⡀⠉⢀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⡜⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⣠⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠋⠁⣠⠴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠉⠛⠶⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣶⠶⠟⠋⠉⣀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣀⡉⠉⠙⠛⠛⠛⠛⠛⠿⠟⠛⠛⠛⠛⠉⠉⠉⣀⣀⡤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠂⠄⠀⠒⠒⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀